Modeling of noise-assisted quantum transfer between donor and acceptor with finite bandwidths

Nesterov, Alexander I.; Berman, Gennady P.; Merkli, Marco; Saxena, Avadh

doi:10.1088/1751-8121/ab4502

Title: Modeling of noise-assisted quantum transfer between donor and acceptor with finite bandwidths

Abstract

We present an analytical and numerical study of noise-assisted quantum exciton (electron) transfer (ET) in a dimer consisting of donor and acceptor, modeled by interacting continuous electron bands of finite widths. We start with discrete energy levels for both bands. The interaction with the environment is modeled by a stationary stochastic process (noise) acting on all the donor and acceptor energy levels. Then, by using a continuous limit for the electron spectra, we derive integro-differential equations for the ET dynamics between the two bands. Finally, we derive from these equations rate-type differential equations for the ET dynamics. We formulate the conditions of validity of the rate-type equations. We consider different regions of parameters characterizing the widths of the donor and acceptor bands and the strength of the dimer-noise interaction. For a simplified model with a single energy level donor and a continuous acceptor band, we derive a generalized simple analytic expression and provide numerical simulations for the ET rate. They are consistent with Wigner–Weisskopf, Förster-type, and Marcus-type expressions, in their corresponding regime of parameters. For a weak dimer-noise interaction, our approach leads to the Wigner–Weisskopf ET rate, or to the Förster-type ET rate, depending on other parameters. In the limitmore »« less

Authors:

^[1]; Berman, Gennady P. ^[2]; Merkli, Marco ^[3];

^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. de Guadalajara, Jalisco (Mexico)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Memorial Univ. of Newfoundland, Newfoundland (Canada)

Publication Date:: Thu Oct 03 00:00:00 EDT 2019

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:: 1768535

Report Number(s):: LA-UR-18-31605
Journal ID: ISSN 1751-8113; TRN: US2206616

Grant/Contract Number:: 89233218CNA000001

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Physics. A, Mathematical and Theoretical

Additional Journal Information:: Journal Volume: 52; Journal Issue: 43; Journal ID: ISSN 1751-8113

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Biological Science

Citation Formats


                    Nesterov, Alexander I., Berman, Gennady P., Merkli, Marco, and Saxena, Avadh. Modeling of noise-assisted quantum transfer between donor and acceptor with finite bandwidths.  United States: N. p., 2019. 
Web.  doi:10.1088/1751-8121/ab4502.

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                    Nesterov, Alexander I., Berman, Gennady P., Merkli, Marco, & Saxena, Avadh. Modeling of noise-assisted quantum transfer between donor and acceptor with finite bandwidths.  United States.  https://doi.org/10.1088/1751-8121/ab4502

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                    Nesterov, Alexander I., Berman, Gennady P., Merkli, Marco, and Saxena, Avadh. Thu .  
"Modeling of noise-assisted quantum transfer between donor and acceptor with finite bandwidths".  United States.  https://doi.org/10.1088/1751-8121/ab4502.  https://www.osti.gov/servlets/purl/1768535.

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@article{osti_1768535,

  title        = {Modeling of noise-assisted quantum transfer between donor and acceptor with finite bandwidths},

  author       = {Nesterov, Alexander I. and Berman, Gennady P. and Merkli, Marco and Saxena, Avadh},

  abstractNote = {We present an analytical and numerical study of noise-assisted quantum exciton (electron) transfer (ET) in a dimer consisting of donor and acceptor, modeled by interacting continuous electron bands of finite widths. We start with discrete energy levels for both bands. The interaction with the environment is modeled by a stationary stochastic process (noise) acting on all the donor and acceptor energy levels. Then, by using a continuous limit for the electron spectra, we derive integro-differential equations for the ET dynamics between the two bands. Finally, we derive from these equations rate-type differential equations for the ET dynamics. We formulate the conditions of validity of the rate-type equations. We consider different regions of parameters characterizing the widths of the donor and acceptor bands and the strength of the dimer-noise interaction. For a simplified model with a single energy level donor and a continuous acceptor band, we derive a generalized simple analytic expression and provide numerical simulations for the ET rate. They are consistent with Wigner–Weisskopf, Förster-type, and Marcus-type expressions, in their corresponding regime of parameters. For a weak dimer-noise interaction, our approach leads to the Wigner–Weisskopf ET rate, or to the Förster-type ET rate, depending on other parameters. In the limit of strong dimer-noise interaction, our approach is non-perturbative in the dimer-noise interaction constant, and it recovers the Marcus-type ET rate. Our analytic results are confirmed by numerical simulations. We demonstrate how our theoretical results are modified when both the donor and the acceptor are described by finite bands. We also show that, for a relatively wide acceptor band, the efficiency of the ET from donor to acceptor can be close to 100% for a broad range of noise amplitudes, for both 'downhill' and 'uphill' ET, for sharp and flat redox potentials, and for reasonably short times. We discuss possible applications of our approach.},

  doi          = {10.1088/1751-8121/ab4502},

  journal      = {Journal of Physics. A, Mathematical and Theoretical},

  number       = 43,

  volume       = 52,

  place        = {United States},

  year         = {Thu Oct 03 00:00:00 EDT 2019},

  month        = {Thu Oct 03 00:00:00 EDT 2019}

}

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Title: Modeling of noise-assisted quantum transfer between donor and acceptor with finite bandwidths

Abstract

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Wave-function approach to Master equations for quantum transport and measurement text, January 2016

Multiscale cyclic dynamics in light harvesting complex in presence of vibrations and noise text, January 2018

Achieving Effective Terminal Exciton Delivery in Quantum Dot Antenna-Sensitized Multistep DNA Photonic Wires journal, July 2013

Chlorophyll d and Acaryochloris marina: current status journal, April 2013

Long-lived quantum coherence in photosynthetic complexes at physiological temperature journal, July 2010

Multiscale cyclic dynamics in light harvesting complex in presence of vibrations and noise journal, January 2019

Femtosecond Visible Transient Absorption Spectroscopy of Chlorophyll f -Containing Photosystem I journal, January 2017

The Theory of Relaxation Processes book, January 1965

Why Quantum Coherence Is Not Important in the Fenna–Matthews–Olsen Complex journal, June 2015

Number-resolved master equation approach to quantum measurement and quantum transport journal, May 2016

From Fluctuations to Phenotypes: The Physiology of Noise journal, December 2006

Uphill energy transfer in a chlorophyll d-dominating oxygenic photosynthetic prokaryote, Acaryochloris marina journal, January 2000

Consistent treatment of coherent and incoherent energy transfer dynamics using a variational master equation journal, September 2011

Polaronic quantum master equation theory of inelastic and coherent resonance energy transfer for soft systems journal, July 2012

Chlorophylls d and f and their role in primary photosynthetic processes of cyanobacteria journal, March 2016

Multimodal Characterization of a Linear DNA-Based Nanostructure journal, January 2012

Environment-assisted quantum transport journal, March 2009

New Insights into the Mechanism of Uphill Excitation Energy Transfer from Core Antenna to Reaction Center in Purple Photosynthetic Bacteria journal, June 2018

Berechnung der nat�rlichen Linienbreite auf Grund der Diracschen Lichttheorie journal, January 1930

Nucleic acid junctions and lattices journal, November 1982

Multi-scale exciton and electron transfer in multi-level donor–acceptor systems journal, August 2017

Temporal fluctuations in the potential energy of proteins: 1/fα noise and diffusion journal, May 2002

Chlorophyll triplet states associated with Photosystem I and Photosystem II in thylakoids of the green alga Chlamydomonas reinhardtii journal, January 2007

Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature
journal, February 2010

Decoherence and Thermalization
journal, March 2007

Superradiance Transition in Photosynthetic Light-Harvesting Complexes
journal, October 2012

Electron transfers in chemistry and biology
journal, August 1985

Real-Time Vibrational Dynamics in Chlorophyll a Studied with a Few-Cycle Pulse Laser
journal, August 2011

A novel construction of complex-valued Gaussian processes with arbitrary spectral densities and its application to excitation energy transfer
journal, June 2013

Corrigendum to: “Influence of phonons on exciton transfer dynamics: comparison of the Redfield, Förster, and modified Redfield equations” [Chem. Phys. 275 (2002) 355–372]
journal, August 2002

Quantum Effects in Biology
book, August 2014

Noise-assisted quantum electron transfer in photosynthetic complexes
journal, July 2013

Multiscale dynamics of open three-level quantum systems with two quasi-degenerate levels
journal, June 2015

Quantum Effects in Biology
journal, January 2019

Protein noises
conference, May 2003

Superradiance Transition in Photosynthetic Light-Harvesting Complexes
text, January 2011

A unified stochastic formulation of dissipative quantum dynamics. II. Beyond linear response of spin baths
journal, January 2018

Theoretical examination of quantum coherence in a photosynthetic system at physiological temperature
journal, October 2009

Protein dynamics and 1/f noise
journal, August 1992

A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations
journal, January 2018

On the adequacy of the Redfield equation and related approaches to the study of quantum dynamics in electronic energy transfer
journal, June 2009

A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems
journal, October 2013

A Novel Construction of Complex-valued Gaussian Processes with Arbitrary Spectral Densities and its Application to Excitation Energy Transfer
text, January 2013

Multiscale dynamics of open three-level quantum systems with two quasi-degenerate levels
text, January 2014

Efficient energy transfer from the long-wavelength antenna chlorophylls to P700 in photosystem I complexes from Spirulina platensis
journal, October 1995

Simulations of the Two-Dimensional Electronic Spectroscopy of the Photosystem II Reaction Center
journal, December 2012

A Structure-Based Model of Energy Transfer Reveals the Principles of Light Harvesting in Photosystem II Supercomplexes
journal, June 2013

Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems
journal, April 2007

Multi-Scale Exciton and Electron Transfer in Multi-Level Donor-Acceptor System
text, January 2014

Dynamics of a chlorophyll dimer in collective and local thermal environments
journal, January 2016

Intrinsic biochemical noise in crowded intracellular conditions
journal, May 2010

Environment-Assisted Quantum Transport
text, January 2008

Zwischenmolekulare Energiewanderung und Fluoreszenz
journal, January 1948

Wave-function approach to Master equations for quantum transport and measurement
journal, December 2016

A coherent modified Redfield theory for excitation energy transfer in molecular aggregates
journal, February 2015

Uphill Energy Trapping by Reaction Center in Bacterial Photosynthesis. 2. Unistep Charge Separation, Virtually Mediated by Special Pair, by Photoexcitation in Place of Excitation Transfer from the Antenna System
journal, August 2004

Architecture of a Charge-Transfer State Regulating Light Harvesting in a Plant Antenna Protein
journal, May 2008

Architecture and mechanism of the light-harvesting apparatus of purple bacteria
journal, May 1998

Uphill Energy Trapping by Reaction Center in Bacterial Photosynthesis: Charge Separation Unistep from Antenna Excitation, Virtually Mediated by Special-Pair Excitation
journal, December 2002

Structure and Interactions of the Chlorophyll a Molecules in the Higher Plant Lhcb4 Antenna Protein
journal, October 2000

Wave-function approach to Master equations for quantum transport and measurement
text, January 2016

Multiscale cyclic dynamics in light harvesting complex in presence of vibrations and noise
text, January 2018

Achieving Effective Terminal Exciton Delivery in Quantum Dot Antenna-Sensitized Multistep DNA Photonic Wires
journal, July 2013

Chlorophyll d and Acaryochloris marina: current status
journal, April 2013

Long-lived quantum coherence in photosynthetic complexes at physiological temperature
journal, July 2010

Multiscale cyclic dynamics in light harvesting complex in presence of vibrations and noise
journal, January 2019

Femtosecond Visible Transient Absorption Spectroscopy of Chlorophyll f -Containing Photosystem I
journal, January 2017

The Theory of Relaxation Processes
book, January 1965

Why Quantum Coherence Is Not Important in the Fenna–Matthews–Olsen Complex
journal, June 2015

Number-resolved master equation approach to quantum measurement and quantum transport
journal, May 2016

From Fluctuations to Phenotypes: The Physiology of Noise
journal, December 2006

Uphill energy transfer in a chlorophyll d-dominating oxygenic photosynthetic prokaryote, Acaryochloris marina
journal, January 2000

Consistent treatment of coherent and incoherent energy transfer dynamics using a variational master equation
journal, September 2011

Polaronic quantum master equation theory of inelastic and coherent resonance energy transfer for soft systems
journal, July 2012

Chlorophylls d and f and their role in primary photosynthetic processes of cyanobacteria
journal, March 2016

Multimodal Characterization of a Linear DNA-Based Nanostructure
journal, January 2012

Environment-assisted quantum transport
journal, March 2009

New Insights into the Mechanism of Uphill Excitation Energy Transfer from Core Antenna to Reaction Center in Purple Photosynthetic Bacteria
journal, June 2018

Berechnung der nat�rlichen Linienbreite auf Grund der Diracschen Lichttheorie
journal, January 1930

Nucleic acid junctions and lattices
journal, November 1982

Multi-scale exciton and electron transfer in multi-level donor–acceptor systems
journal, August 2017

Temporal fluctuations in the potential energy of proteins: 1/fα noise and diffusion
journal, May 2002

Chlorophyll triplet states associated with Photosystem I and Photosystem II in thylakoids of the green alga Chlamydomonas reinhardtii
journal, January 2007